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Nonnegative realization of a linear system with nonnegative impulse response
(1996) Anderson, Brian D.O.; Deistler, Manfred; Farina, Lorenzo; Benvenuti, Luca
Let H (z) be a rational transfer function with associated nonnegative impulse response sequence. The paper considers the question: When does there exist a triple A ε R NXA b ε R N c ε R N with all nonnegative entries and H(z) = c′(zI - A) -1b? An essentially complete characterization is given of the H(z') allowing such a realization in terms of the location of the pole or poles of H(z) with maximum modulus.
Trace element geochemistry of CR chondrite metal
(2013) Jacquet, Emmanuel; Paulhiac-Pison, Marine; Alard, Olivier; Kearsley, Anton T.; Gounelle, Matthieu
We report trace element analyses by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) of metal grains from nine different CR chondrites, distinguishing grains from chondrule interior (interior grains), chondrule surficial shells (margin grains), and the matrix (isolated grains). Save for a few anomalous grains, Ni-normalized trace element patterns are similar for all three petrographic settings, with largely unfractionated refractory siderophile elements and depleted volatile Au, Cu, Ag, S. All three types of grains are interpreted to derive from a common precursor approximated by the least-melted, fine-grained objects in CR chondrites. This also excludes recondensation of metal vapor as the origin of the bulk of margin grains. The metal precursors were presumably formed by incomplete condensation, with evidence for high-temperature isolation of refractory platinum-group-element (PGE)-rich condensates before mixing with lower temperature PGE-depleted condensates. The rounded shape of the Ni-rich, interior grains shows that they were molten and that they equilibrated with silicates upon slow cooling (1-100Kh(-1)), largely by oxidation/evaporation of Fe, hence their high Pd content, for example. We propose that Ni-poorer, amoeboid margin grains, often included in the pyroxene-rich periphery common to type I chondrules, result from less intense processing of a rim accreted onto the chondrule subsequent to the melting event recorded by the interior grains. This means either that there were two separate heating events, which formed olivine/interior grains and pyroxene/margin grains, respectively, between which dust was accreted around the chondrule, or that there was a single high-temperature event, of which the chondrule margin records a late quenching phase, in which case dust accreted onto chondrules while they were molten. In the latter case, high dust concentrations in the chondrule-forming region (at least three orders of magnitude above minimum mass solar nebula models) are indicated.
The formation conditions of enstatite chondrites
(2015) Jacquet, Emmanuel; Alard, Olivier; Gounelle, Matthieu
We report in situ LA-ICP-MS trace element analyses of silicate phases in olivine-bearing chondrules in the Sahara 97096 (EH3) enstatite chondrite. Most olivine and enstatite present rare earth element (REE) patterns comparable to their counterparts in type I chondrules in ordinary chondrites. They thus likely share a similar igneous origin, likely under similar redox conditions. The mesostasis however frequently shows negative Eu and/or Yb (and more rarely Sm) anomalies, evidently out of equilibrium with olivine and enstatite. We suggest that this reflects crystallization of oldhamite during a sulfidation event, already inferred by others, during which the mesostasis was molten, where the complementary positive Eu and Yb anomalies exhibited by oldhamite would have possibly arisen due to a divalent state of these elements. Much of this igneous oldhamite would have been expelled from the chondrules, presumably by inertial acceleration or surface tension effects, and would have contributed to the high abundance of opaque nodules found outside them in EH chondrites. In two chondrules, olivine and enstatite exhibit negatively sloped REE patterns, which may be an extreme manifestation of a general phenomenon (possibly linked to near-liquidus partitioning) underlying the overabundance of light REE observed in most chondrule silicates relative to equilibrium predictions. The silicate phases in one of these two chondrules show complementary Eu, Yb, and Sm anomalies providing direct evidence for the postulated occurrence of the divalent state for these elements at some stage in the formation reservoir of enstatite chondrites. Our work supports the idea that the peculiarities of enstatite chondrites may not require a condensation sequence at high C/O ratios as has long been believed.
In situ measurement of Re-Os isotopes in mantle sulfides by laser ablation multicollector-inductively coupled plasma mass spectrometry
(2001-09-15) Pearson, NJ; Alard, O; Griffin, WL; Jackson, SE; O'Reilly, SY
A method has been developed for the in situ determination of Re-Os isotopes in single grains of sulfides in mantle-derived peridotites using a laser ablation microprobe attached to a multicollector-induced coupled plasma mass spectrometer (MC-ICPMS). High-precision Os isotope analysis by MC-ICPMS is demonstrated by the measurement of interlaboratory Os standards. Evaluation of mass bias correction procedures shows that the exponential law provides the best fit to the Os isotope data and that the ratio of the mass fractionation coefficients for Re and Os remains constant for the range of typical instrument operating conditions, This relationship enables the accurate and precise correction of the isobaric interference of Re-187 on Os-187 for Re-187/Os-188 values up to 1.6.Results are presented for single sulfide inclusions in olivine macrocryts from kimberlites in the Siberian and Slave Cratons, and sulfides enclosed in silicates and interstitial to silicates in peridotite xenoliths from the Slave Craton and Massif Central, France. Enclosed sulfides larger than 50 mum in diameter and with Os contents greater than or equal to40 ppm give Os-187/Os-188 ratios with a precision of 0.1% (2 SE), which is equivalent to N-TIMS whole-rock data. Interstitial sulfides typically have lower Os (10 to 30 ppm) and give analyses with lower precision (similar to1 to 2%) but still provide valuable information on the movement of Os within the lithosphere. The sulfide inclusions in silicates preserve significantly less radiogenic Os isotopic compositions than interstitial sulfides and accordingly produce significantly older and more realistic Re-Os age information. Whole-rock Os isotope compositions reflect the proportions of different generations of enclosed and interstitial sulfides, this calls into question the significance of many published "depletion ages." Copyright (C) 2002 Elsevier Science Ltd.
Detection of photospheric zeeman features and cyclotron emission lines in v834 cen in a low state
(1992) Ferrario, Lilia; Wickramasinghe, D. T.; Bailey, Jeremy; Hough, J. H.; Tuohy, I. R.
We report simultaneous spectroscopic and polarimetric observations of the AM Herculis system V834 Cen during a low state of accretion. The polarization data show a reversal in the sign of the circular polarization when A λ ≳ 5000 A which lasts for about 0.1 in phase and which is not present during a high state. The reversal can be interpreted as the result of dominance of photospheric radiation at these phases. The photometric observations show, for the first time, nearly sinusoidal UBV light curves with minima shifted by 0.5 in phase from previous high-state observations. This behaviour is explained by assuming that the radiation in the blue bands is dominated by blackbody emission from the heated photosphere near the accretion region. The spectroscopic observations show broad, resolvable cyclotron harmonics and strong photospheric Zeeman features. Theoretical models suggest the presence of a dipole of polar field strength Bp≈ 31 MG offset by ≈-0.1 Rwd from the centre of the white dwarf along the dipole axis. The cyclotron emission region is located « 10° from the pole and has B≈ 23 MG.